Maths - Quadratic equations tutorial 1

1. What is a Quadratic Equation?

A quadratic equation is an equation where the highest power of the variable is 2.

General form:

ax^2 + bx + c = 0

Where: $a \neq 0$

and

a, b, c

are numbers

x

is the unknown (variable).

x^2 + 5x + 6 = 0

2x^2 - 7x + 3 = 0

x^2 - 9 = 0

x^3 + 2x = 0

(power is 3 ❌)

Not quadratic: $5x - 4 = 0$ (power is 1 ❌)

For beginners, we learn 3 main methods:

1. Factorisation (easiest)
2. Square root method
3. Quadratic formula

Steps:

1. Write the equation in the form

ax^2 + bx + c = 0

2. Factorise the quadratic expression
3. Set each bracket equal to zero
4. Solve for x

x^2 + 5x + 6 = 0

Step 1: Factorise

Find two numbers that:

Those numbers are 2 and 3

(x + 2)(x + 3) = 0

Step 2: Set each bracket to zero

x + 2 = 0 \quad \text{or} \quad x + 3 = 0

Step 3: Solve for x to get:

x = -2 \quad \text{or} \quad x = -3

✅ Answer: $x = -2, -3$

x^2 - 7x + 10 = 0

Numbers that multiply to +10 and add to –7 are –5 and –2

(x - 5)(x - 2) = 0

Set each bracket equal to zero:

x - 5 = 0

Add 5 to both sides to get $x = 5$

The second bracket:

x - 2 = 0

Add 2 to both sides to get $x = 2$

So $x = 5 \quad \text{or} \quad x = 2$